DeepMaps Model of Labor Force

• DeepMaps Model of the Labor Force is a set of machine learning methods that capture, segment, and forecast labor market dynamics using rigorous statistical and neural techniques.
• It utilizes algorithmic clustering on high-dimensional labor data to produce spatially exhaustive, temporally consistent panels while enforcing strict accounting identities.
• The approach integrates disconnected self-organizing maps, multi-stage data pipelines, and deep learning to generate interpretable, policy-relevant labor market segments.

The DeepMaps model of the labor force encompasses a family of machine learning–driven methods for capturing, segmenting, and forecasting labor market structure and dynamics. These frameworks are characterized by explicit algorithmic clustering of worker or territorial features, rigorous accounting constraints, and the integration of statistical learning and deep neural approaches. Early influential models were based on disconnected self-organizing maps (D-SOM) for micro-level worker clustering (Côme et al., 2015), while contemporary variants incorporate multi-stage data-driven architectures to reconstruct spatially exhaustive, temporally consistent labor panels, adhering to demographic and institutional constraints (Vera-Jaramillo, 17 Aug 2025). DeepMaps thus refers not to a single fixed architecture but to a set of design principles for labor market representation and simulation, including topological segmentation, trajectory analysis, high-dimensional statistical learning, and alignment with macroeconomic and institutional knowledge.

1. Underlying Data Structures and Feature Engineering

DeepMaps frameworks operate directly on high-dimensional labor data, both at the individual worker (micro) and regional or national (meso/macro) levels. In D-SOM implementations, labor force data consists of quantitative variables from survey records, such as hours worked, unemployment duration, earnings (deflated to reference values), multiple job holding, and job tenure. For instance, in the analysis of PSID data, each observation is an 8-dimensional vector, with additional categorical variables for demographic stratification. Preprocessing involves strict validation (removal of implausible records), standardization (zero mean, unit standard deviation), and, for macro-level models, curation of covariates encompassing macroeconomic (e.g., CPI, exchange rate), institutional (e.g., minimum wage, social subsidies), and demographic (population projections) signals, as well as city-level auxiliary series where territorial coverage is incomplete (Vera-Jaramillo, 17 Aug 2025).

2. Architectural Principles and Learning Algorithms

Disconnected Self-Organizing Maps (D-SOM)

D-SOM arranges K code-vectors (neurons) into S disconnected one-dimensional strings (macro-classes), each comprising L_s units. For each input vector $x \in \mathbb{R}^d$, the best matching unit is determined as $i^*(x) = \operatorname{argmin}_i \|x - w_i\|$, with neighboring neurons updated via

$$w_j(t+1) = w_j(t) + \alpha(t)\, h_{ji^*}(t)[x - w_j(t)],$$

where $h_{ji^*}(t) = \exp(-d_G(j,i^*)^2 / 2\sigma(t)^2)$ encodes the graph distance on the D-SOM topology. This structure minimizes extended quantization error and allows explicit macro-class segmentation, with fine gradation along each string (Côme et al., 2015).

Multi-stage Machine and Deep Learning Integration

Contemporary DeepMaps extend these principles via multi-stage modeling pipelines. Temporal disaggregation (e.g., Chow–Lin with AR(1) error structure) converts annual aggregates to monthly trajectories, enforcing exact proportional alignment at multiple aggregation levels. Gradient-boosted trees (XGBoost) predict labor shares (employment rate, unemployment, PEA, inactivity, PET), while custom residual multi-layer perceptrons (MLPs) estimate informality rates, structured with LayerNorm, ReLU activations, dropout, and residual connections (Vera-Jaramillo, 17 Aug 2025). Hyperparameters typically employ default settings for XGBoost and use Adam optimizer with early stopping for MLPs. All models are trained and validated via stratified hold-out and leave-group-out cross-validation.

3. Accounting Identities and National Alignment

A core property of DeepMaps frameworks is the enforcement of labor accounting identities at every point in the data hierarchy. All predicted series satisfy

• $$\mathrm{Employed} + \mathrm{Unemployed} = \mathrm{Labor\,Force}\ (\mathrm{PEA})$$
• $\mathrm{PEA} + \mathrm{Inactive} = \mathrm{PET}$
• $\mathrm{PET} \leq \mathrm{Population}$

Residuals are calculated and reallocated proportionally to guarantee the exactness of these constraints. Completed departmental series are further rescaled to match national monthly aggregates, and informality counts are calibrated for consistency with official totals (Vera-Jaramillo, 17 Aug 2025). No geostatistical interpolation is performed; where direct observation is lacking, donor-region assignment is performed through maximal rank-correlation matching and cluster-based smoothing.

4. Trajectory and Mobility Analysis

DeepMaps originally introduced explicit treatment of individual labor trajectories as Markov chains over map-derived macro-classes. Transition matrices $P_{ij}$ are empirically estimated by counting observed transitions in the longitudinal data. The stationary distributions of these Markov chains provide policy-relevant long-run labor segment shares; for example, the proportion of workers in “good jobs” in the United States, as classified via D-SOM, increased from approximately 37% in the 1980s to 42% in the 1990s. Within-class persistence probabilities remain high (e.g., $P_{55} = 81.2\%$ for “good jobs,” reflecting strong labor market segmentation) (Côme et al., 2015).

5. Cluster Structure and Economic Interpretation

D-SOM macro-classes correspond to economically interpretable labor market segments:

Macro-Class	Employment Intensity	Wage Level	Tenure
Low-activity/unemployed	Very low	Low ($\sim$ \$3.4/h)	Short
High-activity, low-wage	Full-time	Low (\$12/h)	Low
Part-time/withdrawn	Part-year	Medium (\$7.6/h)	Short
Multiple-job workers	Above-average	Above-average (\$14.4/h)	Medium
Good jobs	Full-year	High (\$18.6/h)	Long

This segmentation allows empirical quantification of labor market heterogeneity and the degree of intra- and inter-segment mobility. The macro-class topology is designed to reflect prior labor market segmentation (e.g., 5 sub-markets), and ordering along each segment encodes graduations such as tenure-wage tradeoffs (Côme et al., 2015).

6. Spatial-Temporal Reconstruction and Validation

For applications at national and subnational levels, DeepMaps integrates labor survey series, official benchmarks, and predictive modeling to generate high-frequency, spatially exhaustive panels. For Colombia, monthly labor force indicators are reconstructed for all departments (1993–2025), with informality rates and an Employment Quality Index. All annual departmental aggregates are preserved exactly; out-of-sample MAPEs are consistently below 2.3%, with city-level informality MAPEs near 2.0% (Vera-Jaramillo, 17 Aug 2025).

Validation employs multiple error metrics (MAPE, MAE, RMSE) and stratified temporal and spatial cross-validation. The approach exhibits robust internal coherence, alignment with national benchmarks, and capacity to identify both structural and cyclical labor market variations.

7. Comparative Performance and Theoretical Implications

Relative quantization error (RQE) in D-SOM is minimized compared to classical grid-SOM and star-shaped SOM (SOS), both at the unit and macro-class level (e.g., D-SOM RQE = 12.8% vs. 22.2% for classical SOM). The macro-class organization yields more interpretable and homogeneous clusters and finer gradations within economically meaningful subgroups (Côme et al., 2015). When employed for spatial-temporal labor statistics, the DeepMaps approach, by enforcing exact identities and constrained national alignment, ensures outputs that are not merely predictive but faithful to demographic, institutional, and economic realities (Vera-Jaramillo, 17 Aug 2025). A plausible implication is that DeepMaps models establish a rigorous empirical foundation for monitoring, evaluating, and guiding labor market policy at fine geographic and temporal resolutions.